Design method of transonic turbine blade profile and blade profile

Abstract

This application provides a design method for transonic turbine blade airfoils and the blade airfoil itself, relating to the fields of aero-engine and gas turbine technology. The airfoil is sequentially formed by the leading edge profile, suction front profile, suction trailing profile, trailing edge profile, and pressure profile. The method includes: determining multiple key airfoil control parameters to define the geometric profile and flow channel characteristics of the airfoil; determining the starting and ending positions of each profile based on the key airfoil control parameters; constructing target curves for each profile based on the starting and ending positions, wherein the target curves for the leading edge profile, suction front profile, and suction trailing profile are Bézier curves; and obtaining the blade airfoil based on the target curves of each profile.

Description

Technical Field

[0001] This application relates to the field of aero-engine and gas turbine technology, and in particular to a design method and blade profile for a transonic turbine blade. Background Technology

[0002] Transonic turbine blade design is a key technology developed to address the special operating conditions of modern aero-engines and gas turbines where flow velocities approach or exceed the speed of sound. With the continuous increase in turbine inlet temperature and stage load, traditional subsonic blade design methods can no longer meet the design requirements of high-performance turbines. Shock wave losses and boundary layer separation caused by transonic flow have become the main factors restricting turbine efficiency.

[0003] Currently, transonic airfoil design methods typically use a polynomial curve for the suction surface before the throat and a circular arc for the trailing edge, allowing direct control of the throat area. However, this method has inherent drawbacks: First, the circular arc at the suction exit point causes the backbend angle, throat width, and trailing edge wedge angle to be coupled together, making independent adjustment impossible and reducing design freedom. Summary of the Invention

[0004] In view of this, this application provides a design method for transonic turbine blade airfoils and the blade airfoils themselves.

[0005] One aspect of this application provides a design method for transonic turbine blade profiles. The blade profile is sequentially formed by a leading edge profile, a suction front profile, a suction trailing profile, a trailing edge profile, and a pressure profile. The method includes: determining multiple master control parameters for defining the geometric profile and flow channel characteristics of the blade profile; determining the starting and ending positions of each profile based on the master control parameters; constructing target curves for each profile based on the starting and ending positions, wherein the target curves for the leading edge profile, the suction front profile, and the suction trailing profile are each Bézier curves; and obtaining the blade profile based on the target curves of each profile.

[0006] According to an embodiment of this application, when the target curve is a Bézier curve, the target curve of each profile is constructed based on the starting position and ending position of each profile, including: determining the auxiliary design point position of each profile based on the starting position and ending position of each profile, wherein the auxiliary design point position is the intersection point of the tangents at the starting position and the ending position; determining the polygon used to control the Bézier curve based on the starting position, the auxiliary design point position and the ending position; and constructing the Bézier curve based on the polygon to obtain the target curve.

[0007] According to an embodiment of this application, determining the polygon controlling the Bézier curve based on the starting position, the auxiliary design point position, and the ending position includes: determining a first position range of a first intermediate control point based on a first straight line segment between the starting position and the auxiliary design point position; determining a second position range of a second intermediate control point based on a second straight line segment between the ending position and the auxiliary design point position; adjusting a first weight parameter and a second weight parameter based on the target optimization direction of each curve to determine the target first intermediate control point position on the first straight line segment and the target second intermediate control point position on the second straight line segment, wherein the first weight parameter indicates the distance between the starting position and the first intermediate control point position; the second weight parameter indicates the distance between the ending position and the second intermediate control point position; and determining the polygon based on the starting position, the target first intermediate control point position, the target second intermediate control point position, and the ending position.

[0008] According to an embodiment of this application, when the profile is a leading edge section profile, the first weight parameter and the second weight parameter are adjusted based on the target optimization direction of each profile, including: when the target optimization direction is to reduce the flow resistance coefficient of the leading edge section, the first weight parameter and the second weight parameter are increased to increase the convexity of the leading edge section profile; when the target optimization direction is to improve the variable operating condition adaptability of the leading edge section, the first weight parameter and the second weight parameter are decreased to reduce the convexity of the leading edge section profile.

[0009] According to an embodiment of this application, when the profile is a suction surface rear section profile, the first weight parameter and the second weight parameter are adjusted based on the target optimization direction of each profile, including: when the target optimization direction is to reduce shock wave loss, at least one of the first weight parameter and the second weight parameter is adjusted to adjust the position and width of the aerodynamic throat; wherein, the aerodynamic throat represents the cross-sectional position where the airflow reaches the speed of sound.

[0010] According to an embodiment of this application, the connection point between the front section profile of the suction surface and the rear section profile of the suction surface is located at the geometric throat position of the suction surface, where the geometric throat is the cross-sectional position of the minimum flow area formed by adjacent blades.

[0011] According to an embodiment of this application, two adjacent profile segments are second-order differentiable at the connection point.

[0012] According to embodiments of this application, the main control parameters of the blade profile include axial chord length, number of blades, turning radius and installation angle for defining the axial dimensions and arrangement of the blade profile; inlet angle, outlet angle and backbend angle for defining the airflow direction and blade bending characteristics; leading edge radius, trailing edge radius, leading edge wedge angle and trailing edge wedge angle for defining the local geometry of the leading edge and trailing edge; and throat width for defining the minimum flow area between adjacent blades.

[0013] According to an embodiment of this application, the blade profile is obtained based on the target curves of each profile line, including: calculating the coordinates of multiple discrete points on each profile line based on the parametric equations of each target curve, wherein the number of multiple discrete points is not less than 30, so as to generate the complete blade profile.

[0014] Another aspect of this application provides a transonic turbine blade profile, which is designed according to the method described above.

[0015] According to the technical solution of this application, by constructing the leading edge profile as a Bézier curve, the degree of convexity of the leading edge profile can be precisely and flexibly controlled, thereby accurately adjusting the drag coefficient of the leading edge. By constructing the front and rear sections of the suction surface as Bézier curves, independent and refined geometric adjustments can be made to the curvature distribution of the front section of the suction surface and the shape of the rear section of the suction surface, greatly improving the design freedom of the profile in local geometry, thereby achieving active control over the aerodynamic throat position, shock wave structure and intensity, and reducing transonic airfoil aerodynamic losses. Attached Figure Description

[0016] The above-mentioned contents, other objects, features and advantages of this application will become clearer from the following description of embodiments of this application with reference to the accompanying drawings.

[0017] Figure 1 A schematic diagram of turbine flow channel partitioning according to an embodiment of this application is shown;

[0018] Figure 2 A flowchart illustrating a method for designing transonic turbine blade airfoils according to an embodiment of this application is shown;

[0019] Figure 3 A schematic diagram showing the distribution of blade profile control parameters according to an embodiment of this application is provided;

[0020] Figure 4 A schematic diagram showing the distribution of control points according to an embodiment of this application is shown;

[0021] Figure 5a The diagram shows the effect of the leading edge profile under different weighting parameters according to the embodiments of this application;

[0022] Figure 5b The diagram shows the effect of the suction front end curve under different weighting parameters according to the embodiments of this application;

[0023] Figure 5c The diagram shows the effect of the suction surface rear end curve under different weighting parameters according to the embodiments of this application;

[0024] Figure 6 A schematic diagram of a double throat passage implemented according to this application is shown. Detailed Implementation

[0025] The embodiments of this application will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of this application. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of this application for ease of explanation. However, it will be apparent that one or more embodiments may be implemented without these specific details. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0026] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The terms “comprising,” “including,” etc., as used herein indicate the presence of features, steps, operations, and / or first components, but do not exclude the presence or addition of one or more other features, steps, operations, or first components.

[0027] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0028] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0029] Transonic airfoil design mainly faces the following challenges: First, shock wave control, which requires optimizing the leading edge geometry of the airfoil to reduce the intensity of the shock wave and reasonably control its position; second, boundary layer management, which involves finely controlling the surface curvature distribution to delay flow separation under transonic conditions; and finally, loss mechanism balancing, which involves coordinating the relationship between the airfoil surface velocity distribution and trailing edge losses.

[0030] Typical transonic airfoil design methods include NACA airfoils and polynomial curve methods. These methods can express smooth profiles with fewer parameters, but they lack the ability to directly control the throat area. Therefore, a commonly used design method is Pritchard's 11-parameter method, which divides the suction surface into two curves: a polynomial curve before the throat and a circular arc after the throat, creating a strong geometric constraint. To form a smooth circular arc, the trailing bend angle, throat width, and trailing edge wedge angle must satisfy specific geometric relationships, making these key parameters impossible to adjust independently. This makes it difficult for designers to freely design the trailing edge wedge angle while ensuring the throat area, thus limiting the design freedom of the airfoil.

[0031] In view of this, this application provides a design method for transonic turbine blade airfoils and a blade airfoil, in order to solve at least one of the above-mentioned problems.

[0032] Figure 1 A schematic diagram of turbine flow channel partitioning according to an embodiment of this application is shown.

[0033] like Figure 1 As shown, the flow field is divided into three regions based on flow characteristics. The turbine blade cascade flow field can be divided into region 1, region 2, and region 3. Among them, region 1 is the flow region from the blade inlet to the throat. The characteristic of this channel region is that the airflow continuously accelerates within the effective channel formed by two adjacent blades as the channel width narrows, and the airflow loss is mainly boundary layer loss.

[0034] Region 2 is the flow region from the throat to the blade exit. In this region, the airflow is only affected by the suction surface of the lower blades, meaning it flows only under the viscous force of the lower blades. Airflow control in Region 2 is crucial for transonic turbine blade design. Firstly, an excessively large deflection angle at the suction surface exit section can lead to flow separation. Secondly, under transonic blade flow conditions, the airflow is highly sensitive to the curvature distribution of the profile. Therefore, more refined design is needed to reduce the maximum Mach number and shock wave intensity through proper curvature control.

[0035] Region 3 is the area after the blade trailing edge exit. In this section, the airflow is not affected by the blade, but because the high-speed airflow on the suction side and the low-speed airflow on the pressure side converge here, mixing losses will occur; for transonic blade flow, there will also be shock wave mixing losses.

[0036] Therefore, precise control of the pressure surface curve is the key to reducing aerodynamic losses in blade airfoil design.

[0037] According to an embodiment of this application, the transonic turbine blade profile is formed by the leading edge profile, the suction front profile, the suction trailing profile, the trailing edge profile, and the pressure profile in sequence.

[0038] Figure 2 A flowchart illustrating a method for designing transonic turbine blade airfoils according to an embodiment of this application is shown.

[0039] like Figure 2 As shown, the method includes operations S210 to S240.

[0040] In operation S210, multiple key airfoil parameters are determined to define the geometric profile and flow channel characteristics of the airfoil.

[0041] When operating S220, the starting and ending positions of each profile are determined based on the main control parameters of the airfoil.

[0042] In operation S230, based on the starting and ending positions of each profile, the target curves of each profile are constructed. The target curves of the leading edge profile, the front profile of the suction surface, and the rear profile of the suction surface are each Bézier curves.

[0043] By operating S240, the blade profile is obtained based on the target curves of each profile line.

[0044] The airfoil's master control parameters are pre-defined design variables used to define the basic profile and position of the airfoil. These parameters determine the airfoil's basic dimensions, position, and critical flow capabilities, providing clear boundary conditions for subsequent geometric construction.

[0045] The starting and ending points refer to the coordinates of the two endpoints of each airfoil segment on a two-dimensional plane. They are also the connection points (or transition points) between adjacent airfoil segments. For example, the ending point of the leading edge segment is also the starting point of the suction front segment. All starting and ending points together constitute the basic framework of the airfoil.

[0046] For example, the spatial relationship of the transition points of each airfoil can be determined based on the main control parameters of the airfoil. Based on the spatial relationship of the transition points of each airfoil, the coordinates of one transition point can be defined first, and then the coordinates of other transition points can be determined based on the spatial relationship of the transition points of each airfoil.

[0047] According to embodiments of this application, by constructing the leading edge profile as a Bézier curve, the degree of convexity of the leading edge profile can be precisely and flexibly controlled, thereby accurately adjusting the drag coefficient of the leading edge. By constructing the front and rear sections of the suction surface as Bézier curves, independent and refined geometric adjustments can be made to the curvature distribution of the front section of the suction surface and the shape of the rear section of the suction surface. This greatly enhances the design freedom of the profile in local geometry, thereby achieving active control over the aerodynamic throat position, shock wave structure and intensity, and reducing transonic airfoil aerodynamic losses.

[0048] In some embodiments, the pressure surface profile can be further set as a Bezier curve, and the trailing edge profile can be set as an arc.

[0049] Figure 3 A schematic diagram showing the distribution of blade profile control parameters according to an embodiment of this application is provided.

[0050] like Figure 3 As shown, the main control parameters of the blade profile may include axial chord length (Cx), number of blades (N), radius of rotation (R), and installation angle (ζ) for defining the axial dimensions and arrangement of the blade profile; inlet angle (β1), outlet angle (β2), and backbend angle (δ) for defining the airflow direction and blade bending characteristics; leading edge radius (R1), trailing edge radius (R2), leading edge wedge angle (ψ1), and trailing edge wedge angle (ψ2) for defining the local geometry of the leading and trailing edges; and throat width (O) for defining the minimum flow area between adjacent blades.

[0051] For example, in the initial stage of blade design, the specific values ​​of the above 12 parameters can be determined according to the overall design requirements of the turbine, the flow design results, and the transonic airflow characteristics requirements.

[0052] In this embodiment, the throat width is also treated as an independent design parameter, increasing the degree of design freedom.

[0053] According to an embodiment of this application, when the target curve is a Bézier curve, constructing the target curve for each profile based on the starting and ending positions of each profile may include: determining the auxiliary design point positions for each profile based on the starting and ending positions of each profile, wherein the auxiliary design point positions are the intersection points of the tangents at the starting and ending positions; determining the polygons used to control the Bézier curve based on the starting position, the auxiliary design point positions, and the ending position; and constructing the Bézier curve based on the polygons to obtain the target curve.

[0054] The auxiliary design points constitute the external vertices of the Bézier curve-controlled polygon, and the direction of the Bézier curve-controlled polygon can be determined through the auxiliary design points.

[0055] Figure 4A schematic diagram showing the distribution of control points according to an embodiment of this application is provided.

[0056] like Figure 4 As shown, the positions of transition points p0, p3, p4, p10, and p11 between various airfoils can be calculated based on the main airfoil control parameters. Then, based on the main airfoil control parameters and the positions of the transition points, the positions of four auxiliary design points, p5, p6, p9, and p14, can be determined.

[0057] Taking the determination of the coordinates of p5 as an example, we can first determine the coordinates of p3. The calculation process is as follows:

[0058] X p3 = X p4 +(O+R2)*sin(β2-ψ2+δ);

[0059] Y p3 = Y p4 +2*3.14*R / N–(O+R2)*cos(β2-ψ2+δ);

[0060] Among them, (X) p3， Y p3 () represents the coordinates of p3, (X) p4、 Y p4 () represents the coordinates of p4, O is the throat width, R2 is the trailing edge radius, R is the turning radius, and N is the number of blades.

[0061] Furthermore, solve for the coordinates of p5:

[0062] X p5 =(Y p3 -Y p0 +tan(β1+ζ1)*X p0 -tan(β²-ψ²+δ)*X p3 ) / (tan(β1+ζ1)-tan(β2-ψ2+δ));

[0063] Y p5 =tan(β1+ζ1)*(X p5 -X p0 )+Y p0 .

[0064] Similarly, a similar method can be used to determine the positions of the remaining transition points and the intersections of the tangents.

[0065] According to an embodiment of this application, auxiliary design points are determined by the tangents at the starting and ending positions. Then, based on the starting position, the auxiliary design point position, and the ending position, a polygon for controlling the Bézier curve is determined. This allows the overall trend of the Bézier curve to be highly adapted to the geometric boundary of the airfoil, ensuring the continuity of the profile and preventing the curve shape from becoming disconnected from the basic outline of the airfoil.

[0066] According to embodiments of this application, determining the polygon controlling the Bézier curve based on the starting position, the auxiliary design point position, and the ending position may include: determining a first position range of a first intermediate control point based on a first straight line segment between the starting position and the auxiliary design point position; determining a second position range of a second intermediate control point based on a second straight line segment between the ending position and the auxiliary design point position; adjusting a first weight parameter and a second weight parameter based on the target optimization direction of each curve to determine the target first intermediate control point position on the first straight line segment and the target second intermediate control point position on the second straight line segment, wherein the first weight parameter indicates the distance between the starting position and the first intermediate control point position; the second weight parameter indicates the distance between the ending position and the second intermediate control point position; and determining the polygon based on the starting position, the target first intermediate control point position, the target second intermediate control point position, and the ending position.

[0067] The first straight segment is the only possible distribution range for the first intermediate control point, and the first intermediate control point can only move within this straight segment. Similarly, the second straight segment is the only possible distribution range for the second intermediate control point, and the second intermediate control point can only move within this straight segment.

[0068] The first weighting parameter can be the ratio of the distance between the starting point and the first intermediate control point to the distance between the starting point and the auxiliary design point. The larger the parameter value, the closer the first intermediate control point is to the auxiliary design point; the smaller the parameter value, the closer it is to the starting point.

[0069] Similarly, the second weighting parameter can be the ratio of the distance between the endpoint and the first intermediate control point to the distance between the endpoint and the auxiliary design point. The larger the parameter value, the closer the second intermediate control point is to the auxiliary design point; the smaller the parameter value, the closer it is to the endpoint.

[0070] like Figure 4 As shown, the positions of intermediate control points p1, p2, p7, p8, p13, p12, p15, and p16 can be determined based on the weight parameters, the positions of transition points p0, p3, p4, p10, and p11 between each profile, and the positions of auxiliary design points p5, p6, p9, and p14.

[0071] Taking the determination of the positions of P1 and P2 as an example, the calculation process is as follows:

[0072] X p1 = X p0 + LLS1 * (X p5 -X p0 );

[0073] Y p1 = Y p0+ LLS1 * (Y p5 -Y p0 );

[0074] X p2 = X p3 + LLS2 * (X p5 -X p3 );

[0075] Y p2 = Y p3 + LLS2 * (Y p5 -Y p3 );

[0076] Here, LLS1 represents the first weight parameter, and LLS2 represents the second weight parameter. Similarly, the positions of p7 and p8 can be determined based on the weight parameters LLS5 and LLS6, the positions of p12 and p13 can be determined based on the weight parameters LLP1 and LLP2, and the positions of p15 and p16 can be determined based on the weight parameter LLE1.

[0077] Figure 5a The diagram shows the effect of the leading edge profile under different weighting parameters according to the embodiments of this application. Figure 5b The diagram shows the effect of the suction front end curve under different weighting parameters according to the embodiments of this application; Figure 5c The diagram shows the effect of the suction surface rear end curve under different weight parameters according to the embodiments of this application.

[0078] like Figures 5a-5c As shown, if the weight parameter is small, the curve will be relatively flat and close to the chord; if the weight parameter is large, the curve will be more convex.

[0079] For example, the adjustment trend and specific values ​​of the first weight parameter and the second weight parameter can be determined according to the target optimization direction of each line segment; based on the adjusted weight parameters, the positions of the target first intermediate control point and the target second intermediate control point are calculated on the first line segment and the second line segment.

[0080] For example, aerodynamic simulation can be performed on the airfoil with each weight parameter determined, and the optimal weight parameters can be determined based on the simulation results.

[0081] According to embodiments of this application, by setting adjustable intermediate control points on the lines connecting the starting point and auxiliary points, and the ending point and auxiliary points, and by introducing weight parameters, designers can precisely control the degree to which the curve deviates from the polygon, thereby locally and accurately adjusting the curvature distribution of the profile.

[0082] According to an embodiment of this application, when the profile is a leading edge section profile, adjusting the first weight parameter and the second weight parameter based on the target optimization direction of each profile may include: increasing the first weight parameter and the second weight parameter when the target optimization direction is to reduce the flow resistance coefficient of the leading edge section, so as to increase the convexity of the leading edge section profile; and decreasing the first weight parameter and the second weight parameter when the target optimization direction is to improve the variable operating condition adaptability of the leading edge section, so as to reduce the convexity of the leading edge section profile.

[0083] The shape of the leading edge directly affects the airflow angle of attack adaptability and leading edge loss. By increasing the first and second weighting parameters, the generated Bezier curve can be made more prominent, reducing the airflow acceleration gradient near the leading edge, decreasing the peak suction at the leading edge, and thus reducing the drag coefficient.

[0084] By reducing the first and second weighting parameters, the generated Bezier curve can be made smoother, thereby maintaining lower losses over a wider angle of attack range and improving performance under varying operating conditions.

[0085] According to embodiments of this application, by adjusting the weights corresponding to different target optimization directions, designers can easily weigh different aerodynamic requirements and achieve customized design of the leading edge shape.

[0086] According to an embodiment of this application, the connection point between the front section profile and the rear section profile of the suction surface is located at the geometric throat position of the suction surface. The geometric throat is the cross-sectional location of the minimum flow area formed by adjacent blades.

[0087] The suction surface curve is divided into two segments in the geometric throat. The front section of the suction surface is used to accelerate the airflow, while the rear section of the suction surface is used to deflect and diffuse the airflow.

[0088] According to an embodiment of this application, by setting the connection point at the beginning of the geometric throat, the profile before and after the throat can be controlled independently, thereby facilitating targeted aerodynamic optimization.

[0089] According to an embodiment of this application, two adjacent profile segments are second-order differentiable at the connection point.

[0090] By ensuring that two adjacent airfoil segments are second-differentiable at their junction, the curvature continuity of the entire airfoil can be guaranteed. This ensures that the pressure gradient does not change abruptly, thereby avoiding boundary layer separation or shock wave enhancement induced by geometric discontinuities, improving flow smoothness, and reducing additional losses.

[0091] According to an embodiment of this application, when the profile is the rear section profile of the suction surface, adjusting the first weight parameter and the second weight parameter based on the target optimization direction of each profile may include: when the target optimization direction is to reduce shock wave loss, adjusting at least one of the first weight parameter and the second weight parameter to adjust the position and width of the aerodynamic throat.

[0092] Figure 6 A schematic diagram of a double throat passage implemented according to this application is shown.

[0093] like Figure 6 As shown, for turbine blade cascades, in addition to the aforementioned geometric throat (O), an aerodynamic throat can also be determined at the cross-section where the airflow reaches the speed of sound. The ratio of the width of the geometric throat to that of the aerodynamic throat determines the expansion wave-shock wave system structure of the transonic turbine, thus affecting its aerodynamic performance.

[0094] When the target optimization direction is to reduce shock wave loss, the size and position of the aerodynamic throat can be controlled by adjusting the weight parameters LLS5 and LLS6. In this way, the intensity of the outlet diffuser flow can be precisely controlled by controlling the ratio of the aerodynamic throat to the geometric throat, thereby reducing the aerodynamic loss of the transonic airfoil.

[0095] The size of the aerodynamic throat directly affects the intensity and angle of the trailing edge shock wave. Properly matching the width of the dual throats can weaken the shock wave intensity or push it out of the trailing edge, reducing interference losses between the shock wave and the boundary layer. The aerodynamic throat can also determine the degree of airflow expansion at the blade exit, ensuring that the airflow exits at the designed angle and reducing lag angle deviation. Furthermore, by controlling the position of the aerodynamic throat, the distribution of Mach number on the blade surface can be altered, particularly the location of the peak Mach number, preventing excessively strong shock-induced boundary layer separation.

[0096] According to an embodiment of this application, obtaining the blade profile based on the target curve of each profile may include: calculating the coordinates of multiple discrete points on each profile based on the parametric equation of each target curve, wherein the number of multiple discrete points is not less than 30, in order to generate the complete blade profile.

[0097] For example, the Bézier curve in this application can be a third-order Bézier curve. Taking the solution of the coordinate points of the front section profile of the suction head as an example, assuming that n coordinate points are evenly distributed on the curve, the i-th coordinate point (X) on the curve is obtained according to the Bezier curve polygon (composed of p10, p12, p13 and p11). P(i) Y P(i) ):

[0098] X p(i) =(1-(i-1) / (n-1)) 3 *X p10+3*(i-1) / (n-1)*(1-(i-1) / (n-1)) 2 *X p12 +3*((i-1) / (n-1)) 2 *(1-(i-1) / (n-1))*X p13 +((i-1) / (n-1)) 3 *X p11 ;

[0099] Y p(i) =(1-(i-1) / (n-1)) 3 *Y p10 +3*(i-1) / (n-1)*(1-(i-1) / (n-1)) 2 *Y p12 +3*((i-1) / (n-1)) 2 *(1-(i-1) / (n-1))*Y p13 +((i-1) / (n-1)) 3 *Y p11 ;

[0100] Among them, (X) p10 Y p10 (X) represents the coordinates of p10. p12 Y p12 (X) represents the coordinates of p12. p13 Y p13 (X) represents the coordinates of p13. p14 Y p14 ) represents the coordinates of p14.

[0101] The calculation using the parametric equations of the Bézier curve only requires 30 discrete points, which can better balance computational efficiency and geometric fidelity of the profile.

[0102] Another aspect of this application provides a transonic turbine blade profile, which is designed according to the method described above.

[0103] Those skilled in the art will understand that the features described in the various embodiments of this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, the features described in the various embodiments of this application can be combined and / or combined in various ways without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application.

[0104] The embodiments of this application have been described above. However, these embodiments are merely illustrative and not intended to limit the scope of this application. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. Without departing from the scope of this application, those skilled in the art can make various substitutions and modifications, all of which should fall within the scope of this application.

Claims

1. A method of designing a transonic turbine blade profile, characterized by, The blade profile is formed by the sequential arrangement of the leading edge profile, the front suction surface profile, the rear suction surface profile, the trailing edge profile, and the pressure surface profile. The method includes: Determine multiple key airfoil parameters that define the geometric profile and flow channel characteristics of the airfoil; Based on the aforementioned blade profile control parameters, determine the starting and ending positions of each profile line; Based on the starting and ending positions of each profile, a target curve for each profile is constructed, wherein the target curves for the leading edge profile, the front section profile of the suction surface, and the rear section profile of the suction surface are each Bézier curves. The blade profile is obtained based on the target curves of each profile line.

2. The method of claim 1, wherein, When the target curve is a Bézier curve, constructing the target curve for each type of curve based on the starting and ending positions of each curve includes: Based on the starting and ending positions of each profile line, the auxiliary design point positions of each profile line are determined. The auxiliary design point positions are the intersection points of the tangents at the ending and starting positions, respectively. Based on the starting point position, auxiliary design point position, and ending point position, determine the polygon used to control the Bézier curve; Based on the polygon, a Bézier curve is constructed to obtain the target curve.

3. The method of claim 2, wherein, The process of determining the polygon controlling the Bézier curve based on the starting point position, the auxiliary design point position, and the ending point position includes: Based on the first straight line segment between the starting point position and the auxiliary design point position, determine the first position range of the first intermediate control point; Based on the second straight line segment between the endpoint position and the auxiliary design point position, determine the second position range of the second intermediate control point; Based on the target optimization direction of each type of line, the first weight parameter and the second weight parameter are adjusted to determine the position of the first intermediate control point on the first straight line segment and the position of the second intermediate control point on the second straight line segment. The first weight parameter indicates the distance between the starting position and the first intermediate control point position; the second weight parameter indicates the distance between the ending position and the second intermediate control point position. The polygon is determined based on the starting position, the first intermediate control point position, the second intermediate control point position, and the ending position.

4. The method of claim 3, wherein, When the profile is a leading edge segment profile, adjusting the first weight parameter and the second weight parameter based on the target optimization direction of each profile includes: When the target optimization direction is to reduce the flow resistance coefficient of the leading edge segment, the first weight parameter and the second weight parameter are increased to increase the convexity of the leading edge segment profile. When the target optimization direction is to improve the adaptability of the leading edge segment to different operating conditions, the first weight parameter and the second weight parameter are reduced so as to reduce the convexity of the leading edge segment profile.

5. The method of claim 3, wherein, When the profile is the rear section profile of the suction surface, the adjustment of the first weight parameter and the second weight parameter based on the target optimization direction of each profile includes: When the target optimization direction is to reduce shock wave loss, at least one of the first weight parameter and the second weight parameter is adjusted to adjust the position and width of the aerodynamic throat; wherein the aerodynamic throat represents the cross-sectional position where the airflow reaches the speed of sound.

6. The method according to any one of claims 1 to 5, characterized in that, The connection point between the front section profile and the rear section profile of the suction surface is located at the geometric throat of the suction surface, and the geometric throat represents the cross-sectional position of the minimum flow area formed by adjacent blades.

7. The method according to any one of claims 1 to 5, characterized in that, Two adjacent curve segments are differentiable at their connection point.

8. The method according to any one of claims 1 to 5, characterized in that, The main control parameters of the airfoil include axial chord length, number of blades, radius of rotation, and installation angle, which are used to limit the axial dimensions and arrangement of the airfoil; inlet angle, outlet angle, and backbend angle, which are used to limit the airflow direction and the bending characteristics of the blades; and leading edge radius, trailing edge radius, leading edge wedge angle, and trailing edge wedge angle, which are used to limit the local geometry of the leading and trailing edges. And the throat width used to define the minimum flow area between adjacent blades.

9. The method according to any one of claims 1 to 5, characterized in that, The blade profile is obtained based on the target curves of each profile line, including: The coordinates of multiple discrete points on each profile are calculated based on the parametric equations of each target curve, with the number of such discrete points being no less than 30, in order to generate the complete blade profile.

10. A transonic turbine blade profile, characterized in that, The blade shape is designed according to any one of the methods described in claims 1 to 8.

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